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Mathematical Underpinnings of Analytics

Peter Grindrod
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
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Analytics, according to the author, refers to “the concepts, methods, and practices that can conjure valuable and actionable insights and radical knowledge” from large volumes of data. In this book that amounts to the application of mathematical tools to big data sets, largely in the commercial world, to identify actions that lead to competitive advantage. Amplifying this further, the author writes: “The key challenge for those of us researching, working with, and exploiting analytics is to produce insights that are data-driven, are usually hidden at first sight, and reflect some knowledge that is novel or private to the data owner, and thus advantageous.”

The book’s target audience includes mathematicians, scientists in quantitative disciplines, and engineers. It is written at a level accessible to advanced undergraduates or beginning graduate students. Desirable prerequisites include calculus, linear algebra, basic differential equations and some probability. The primary mathematical tools used in the book are discrete mathematics (mostly graphs and networks), probability and statistical inference, optimization and system dynamics.

The author notes that he has selected topics to match his own interests, so the potential reader should understand that this is not a broad look at mathematical methods for data analysis. Instead, for each selected area, a mathematical framework is introduced with some corresponding theory and this is followed by illustrative applications that point out strengths and weaknesses of various approaches.

Much of the book deals with mathematical tools applicable to analysis of social media and digital marketing networks. For example, one chapter focuses on centrality measures for dynamically evolving networks. The motivation here is to identify individuals in a social network who are most influential. Another chapter looks at peer-to-peer networks and describes techniques for identifying key influencers.

With virtually all mathematical techniques discussed — no matter how broad their potential applicability — the emphasis is on commercial applications. For example, cluster analysis is motivated by a need to assess credit worthiness. Multiple hypothesis testing is used to identify mobile phone users who switch services frequently to take advantage of promotional offers. Adaptive forecasting predicts sales following product launches. Markov models are introduced to attempt to capture changing models of customer behavior.

This unrelenting emphasis on commerce and marketing may appeal to some readers, but others may not find it to their taste. There are a few other examples — to proteomics-genomics and energy usage — but digital marketing concerns dominate.

Two other texts that treat many of the same topics from a broader perspective than the current book are The Elements of Statistical Learning by Trevor Hastie et al., aimed at readers with some advanced training in mathematics and statistics, and Introduction to Statistical Learning by Gareth James et al., which is less technical and has more emphasis on applications. Earlier editions of both of these are available for free download.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

Introduction: The Underpinnings of Analytics
1. Similarity, Graphs and Networks, Random Matrices and SVD
2. Dynamically Evolving Networks
3. Structure and Responsiveness
4. Clustering and Unsupervised Classication
5. Multiple Hypothesis Testing Over Live Data
6. Adaptive Forecasting
7. Customer Journeys and Markov Chains
Appendix: Uncertainty, Probability and Reasoning